The models discussed in this paper are based on a couple of general physical principles and contain very few parameters. The principles are the CEP and the related argument that localized objects are constrained states of a finite dimensional quantum system that lives on the instantaneous horizon of causal diamonds in the universe. These lead to the general principle we have used throughout: choose cosmological initial conditions of highest probability in the space of quantum states, consistent with the existence of long lived localized objects. We argued that these principles lead inevitably to a slow roll inflationary cosmology, which terminates in a dilute gas of black holes whose average Schwarzschild radius is the inflationary horizon. The quantum statistical fluctuations in the individual black hole states lead to the observed CMB fluctuations. Recent work[1]} has enabled us to tie down the form of these fluctuations more precisely. They fit the CMB data if we impose the additional requirement of approximate \(SO(1,4)\)  invariance. This cannot be derived from our general principles, but the conjecture that black hole horizons are described by an approximate \(1 + 1\)  dimensional CFT, implies that fluctuations are scale invariant in each direction in the sky. The predictions of these models are distinct from predictions of field theory inflation models and a measurement of tensor modes may be enough to decide which kind of model is correct. On a more theoretical level, field theory models violate the CKN bound[2]}[3]} on the validity of field theory in finite causal diamonds, while models based on the CEP automatically satisfy that bound.
